Ultra-high-resolution observations of persistent null-point reconnection in the solar corona

Magnetic reconnection is a key mechanism involved in solar eruptions and is also a prime possibility to heat the low corona to millions of degrees. Here, we present ultra-high-resolution extreme ultraviolet observations of persistent null-point reconnection in the corona at a scale of about 390 km over one hour observations of the Extreme-Ultraviolet Imager on board Solar Orbiter spacecraft. The observations show formation of a null-point configuration above a minor positive polarity embedded within a region of dominant negative polarity near a sunspot. The gentle phase of the persistent null-point reconnection is evidenced by sustained point-like high-temperature plasma (about 10 MK) near the null-point and constant outflow blobs not only along the outer spine but also along the fan surface. The blobs appear at a higher frequency than previously observed with an average velocity of about 80 km s−1 and life-times of about 40 s. The null-point reconnection also occurs explosively but only for 4 minutes, its coupling with a mini-filament eruption generates a spiral jet. These results suggest that magnetic reconnection, at previously unresolved scales, proceeds continually in a gentle and/or explosive way to persistently transfer mass and energy to the overlying corona.

of fragmented current elements (or magnetic islands) of different scales, likely arising from tearing mode instability and turbulence [16][17][18][19][20]. Intermittent sunward outflow jets with a wide velocity distribution provide a strong indicator of fragmention of the large-scale current sheet [4]. Similar processes were also believed to occur during small-scale reconnection events in the lower atmosphere [21][22][23]. Using high resolution Hα images from the groundbased New Vacuum Solar Telescope (NVST) [24], it was clearly observed that plasmoids are expelled out of small-scale reconnection regions intermittently [25,26].
Magnetic reconnection is also a promising candidate for releasing the energy to heat the corona to millions of degrees [27,28]. Taking advantage of extreme-ultraviolet (EUV) imaging data from the High-resolution Coronal Imager (Hi-C), which ideally is able to resolve scales on the order of 150 km, Ref [29] provided evidence for reconnection between braided magnetic threads and corresponding heating [30,31]. Using the Imaging Magnetograph eXperiment (IMaX) instrument [32] on board SUNRISE [33], with a spatial resolution of about 80 km, Ref [34] found that active-region coronal loops could be located in regions where small-scale opposite polarities cancel with the dominant polarity and inverse Y-shaped jets are frequently ejected. The two features strongly indicate that cancellation-driven smallscale reconnection plays a vital role in transferring energy and mass into the coronal loops [35,36].
Here, we report a small-scale null-point reconnection event observed by the EUV High Resolution Imager (HRI EUV ) 174Å of the Extreme Ultraviolet Imager (EUI) [37] on board Solar Orbiter (SolO) [38] on 2022 March 3 as located at a distance of 0.55 AU from the Sun. High spatio-temporal resolution images of the HRI EUV revealed that the reconnection driven by a moving magnetic feature takes place continuously at the null-point, at previously unresolved scales, over the period (one hour) of the EUI observation.

Persistent Null Reconnection
In the high-resolution HRI EUV 174Å images, a point-like brightening with a spatial scale of about 390 km (two pixels) is visible throughout the sequence (Figures 1 and 2a-2f).
The Helioseismic and Magnetic Imager (HMI) [39]   All times have been corrected to that at the Earth. g-r. Same as panels a-f but for the IRIS 1330 A slit-jaw images (g-l) and DEM-weighted average temperature maps (m-r). s-x. The AIA 171Å images of persistent reconnection at the null-point (s-u) and spiral jet (v-x), the contours (±100G) of the HMI LOS magnetogram at the same time are overlaid in panel s with white (gray) indicating positive (negative) polarity. The point-like brightening indicating the null-point is pointed out by the white arrows in panels a-c, h-i, s-u. The spiral jet, leading front of the erupting filament, and induced bright loops are indicated by the grey arrows in panels e and w.
that the point-like brightening is located above a minor isolated positive polarity embedded within the main negative polarity (Figure 2s). These features suggest that the magnetic structure consists of a magnetic dome enclosing the flux that connects to the isolated positive polarity and separating that flux from the surrounding negative polarity. This is confirmed by extrapolating the three-dimensional (3D) coronal potential magnetic field structure from an observed photospheric magnetogram (Figure 3), which clearly shows that there is indeed a dome containing a 3D null-point and representing the fan separatrix surface of magnetic field lines that spread out from the null. Justification for the potential extrapolation is given in Section IV. In addition, two isolated spine field lines approach the null from above and below. The cospatiality between the point-like brightening and the null-point strongly indicates that the reconnection takes place near the null-point at the intersection of the spine and fan as in the theory of Ref [40]. Such a structure corresponding to the field around a 3D magnetic null-point has also been suggested for a UV burst close to the photosphere [41,42], for jets at the base of coronal plumes or equatorial coronal-holes [43,44] and for a flare with circular ribbons [45,46].
In our case, the point-like brightening also occasionally shows up in the Interface Region Imaging Spectrograph (IRIS) [47] 1330Å images in spite of being more tenuous ( Fig. 2), lower than that of the null-point associated brightening. These persistent blobs were also detected to come out at the jet base and then move upward in the polar coronal hole [49]. We made two distance-time plots to track the trajectories of these blobs. Figure 4a shows that the blobs move outward along the spine (slit S1 in Figure 2c). Figure 4b indicates that the blobs move along the inclined direction (slit S2), from which we detected bidirectional motions. After identifying the positions of the fast-moving blobs manually in distance-time plots (dotted lines in Figure   4a and 4b), we estimated their linear velocities and lifetimes, the histograms of which are displayed in Figure 4c and 4d, respectively. We find that the velocity of the blobs ranges but also transfers magnetic twist to the overlying field as suggested by Ref [55]. Thanks to the better spatial resolution and temporal cadence, these detailed dynamical processes for the spiral jet were more clearly captured by the HRI EUV than by the AIA. In addition, no evidence was found to support that the preceding null-point reconnection plays a role in triggering the mini-filament eruption and causes the spiral jet as argued previously [43,44,56,57] given the null-point reconnection remained sustained after the eruption (Figure 4a and 4b).

Light Curves of Null Reconnection and Spiral Jet
Although reconnection near the null-point was persistent, it seemed to vary in time. This is indicated by a number of spikes with different amplitudes appearing in the time profile of the HRI EUV 174Å integrated intensity (the black curve in Figure 5b), which was derived by integrating a small region only including the null-point (Box 1 in Figure 5a). In contrast, only some big spikes are detectable in the AIA 171Å integrated intensity curve of the same region (the grey curve in Figure 5b). The two spikes during the time period of 10:12-10:14 UT even appear to be higher than that in the HRI EUV 174Å curve. This might be caused by a temperature effect. In general, hotter plasma has the tendency to show less variability, and the AIA 171Å passband samples slightly cooler plasma (mainly Fe IX emission) than the HRI EUV 174Å passband (mostly Fe X). Moreover, we also calculated the 174Å integrated intensity, as well as the AIA 94Å, 171Å and 304Å ones, over the whole fan and spine structure (Box 0). It is found that only a few large spikes were able to be identified in the AIA 171Å and 304Å light curves. For the AIA 94Å light curve, no such spikes can be detected. This discrepancy demonstrates a need for EUV imaging with a spatial resolution better than an arcsecond and a time cadence higher than 10 s to resolve the fine structures of small-scale events in the corona and disclose their hidden dynamics [58]. Figure 5c shows the temporal variations of the HRI EUV 174Å intensities at three regions during the jet eruption (Box 2-4 in Figure 5a). One can see that the brightenings first appeared at Box 2 and 3, even though not strong. Starting with 10:12 UT, the intensities at all three regions quickly increased and lasted for at least 5 minutes, even for almost 10 minutes at Box 2. Comparing to Box 2 and 3, the peak of the intensity at Box 4 was delayed by 1.5 min, which may be caused by the external fan reconnection commencing after the inner reconnection below the mini-filament. These features again imply that the erupting mini-filament have experienced multiple reconnection processes as it broke through the null-point-associated fan surface.
Note that the spikes of the HRI EUV 174Å emission from the null-point reconnection seem to be invisible after the jet eruption (Figure 5b; 10:16 UT), but the fast moving plasma blobs are still detectable as shown in Figure 4a and 4b. It implies that, even though the heating may be weakened, the null-point reconnection is still ongoing. This is also indicated by the long-term stability of the null-point and persistent plasma heating after the jet eruption ( Supplementary Videos 3 and 4).

Driver of Null Reconnection and Spiral Jet
To explore the reasons for the persistent null reconnection and spiral jet eruption, we investigated the long-term evolution of the HMI LOS and vector magnetograms. It was found that the reconnection and jet were closely related to the movement of the minor positive polarity. Highly resembling a typical moving magnetic feature [59][60][61], it rapidly emerged within the negative-polarity penumbra and was then carried outward by the moat flow of the sunspot. We calculated the total flux of the minor positive polarity over the region where the magnetic field strength is larger than 10 G (i.e., above the typical noise level in the HMI line of sight magnetograms). Moreover, we also estimated the height of the null-point during the entire lifetime of the minor positive polarity. Figure 6a shows that the null-point quickly ascends (descends) along with the emergence (submergence) of the minor positive polarity before 07:00 UT (after 11:00 UT). During the time period of 07:00-11:00 UT, even though the height of the null-point only slightly declines, the total flux varies violently, which mainly originates from the interaction of the fast emerging/moving minor positive polarity with the nearby moss region. Meanwhile, the fast movement may also provide a direct driver for continuous reconnection at the null-point.
Furthermore, during the early emergence phase, the flux carried a certain magnetic twist as deduced from the appearance of bald patches (BPs), which represent unusual sections of the photospheric polarity inversion line (PIL) where the twisted field touches the photosphere tangentially [62]. Such twisted field over the PIL often gives rise to filaments or mini-filaments at their dips and represent locations where magnetic free energy is stored. Figure 6b shows that the BPs (red curves) are mainly distributed along the south part of the PIL (green curves). As the time lapsed, the BPs concentrated toward the south. They did not start to disappear until after 11:00 UT. The deduction of magnetic twist is further confirmed by the appearance of a mini-filament that is almost co-spatial with the BPs, in particular during the time period before the jet eruption (Figure 6c). Moreover, the mini-filament also displays a blueshift feature (Figure 6c), which suggests that the mini-filament was ascending in height and then erupted to cause the jet once destabilized. The null-point and fan-spine configuration have been observed in flares [44-46, 63, 64] and at the base of coronal plumes or equatorial coronal-holes [43,44]. In previous studies, although the null-point reconnection was observed to occur repetitively sometimes, the highest occurrence rate was found to be only about once every three to five minutes [44]. Using the EUI/HRI EUV data, it was revealed that the null-point reconnection at scales previously unresolved proceeds almost continuously with hot blobs expelled much more frequently. After carefully examining the time-sequence of HMI magnetograms, we suggest that various motions at the photosphere, such as the fast flux movement observed here, may provide a direct driver for the persistence of magnetic reconnection.
The finding of persistent minor null-point reconnection sheds an important light on the solution of the coronal heating problem. As revealed by SUNRISE II, minor smallscale opposite-polarity fluxes are prevalent at the periphery of the penumbra in the moat around a sunspot [34]. In quiet-Sun regions, opposite-polarity fluxes frequently appear within dominant flux concentrations although they may be short-lived [65,66]. We tentatively calculated the topology of the potential field over a larger quiet-Sun region nearby the nullpoint studied currently and found abundant low-lying small-scale null-points, consistent with previous explorations [67][68][69]. Our observations thus support to find even smaller and more frequent null-point reconnection events, in particular over the quiet-Sun region, hopefully with the further increase of the spatio-temporal resolution of EUV imaging, such as when the SolO approaches the closest perihelion. As driven by constant photospheric turbulent flows, it is reasonable to conjecture that the reconnection at smaller-scale nullpoints possibly occurs ubiquitously so as to heat the low corona. Assuming all fluxes are dissipated through this type of null-point reconnection driven by cancelling flux, based on the estimation given by Ref [35], the heating per unit area is 5 × 10 6 erg cm −2 sec −1 in the Quiet Sun and is 5 × 10 7 erg cm −2 sec −1 in an active region, respectively, which are sufficient to heat the chromosphere. If 10% -20% of this leaks to higher levels it would be sufficient for heating the low corona [70].
Except for the quasi-stable and persistent nature, the null-point reconnection also occurs impulsively but with a short-time period. Its coupling with the eruption of a mini-filament produced a spiral jet, which more quickly transferred mass and magnetic twist to the higher corona as interpreted in Figure 7c. The more details revealed during the dynamic reconnection phase support recent observations [57] and 3D MHD modelling of spiral jets [56,71], which suggested that a slowly rising mini-flux rope reconnects with the inclined overlying field near a null-point, which may collapse into a breakout current sheet during the eruption [45,71,72], and the helical flux is released to the overlying field as a spiral jet. A careful inspection found the appearance of continuous BPs and a co-spatial mini-filament in Hα images, which provides a solid evidence for the existence of a mini-magnetic flux rope that is often presupposed in previous studies.

Methods
Instruments and data. We mainly used the EUI/HRI EUV 174Å level 2 data [82]. The AIA and HMI are both on board the Solar Dynamics Observatory (SDO) [74]. The pixel size and cadence of the AIA are 0.6 (linear scale of 420 km) and 12 s, respectively.
The calibrated HMI images have the same pixel size as the AIA images, but the cadence is We have also tested the reliability of the DEMs through 200 Monte Carlo (MC) simulations, which are done by adding a random noise to observed intensities and rerunning the procedure again. Supplementary Fig. 1 Supplementary Fig. 2, which displays that the result is well constrained in the temperature range of 5.5≤ logT ≤ 6.9. The DEM-weighted average temperature is about 2 MK. The density n is estimated by where l is the depth of the blob along the LOS. Assuming the depth of the blob approximates its width (about 0.5 Mm), the density is calculated to be about 5 × 10 9 cm −3 .
Thermal energy estimation. The thermal energy flow F caused by the reconnection outflow blobs is estimated by and the enthalpy density e is where internal energy flow F is estimated to be about 1.2 × 10 5 erg · cm −2 · s −1 , which accounts for approximately 40% of the total energy flow required for heating the quiet-Sun corona. In comparison, the kinematic energy is negligible after estimation following the same procedure.
3D magnetic field and topology computation. We calculate the 3D coronal magnetic field from a potential field extrapolation based on the radial component of the HMI vector field as the bottom boundary. The locations of null-point and fan-spine are computed by the method in Ref [78]. In the current case, considering the lack of observations of electric currents for the small-scale region of interest, we only take advantage of the potential field model. Overall, the potential field method is good enough given the cospatiality between the observed point-like brightening and extrapolated null-point and the agreement between the whole dome-like structure and the extrapolated fan surface. In fact, the null-point is a topologically rather-stable feature as confirmed by its long-term existence in the current event ( Figure 6a). It is also shown that the appearance of observed current concentrations below the fan-surface cannot destroy the null-point [46,79], usually only giving rise to a displacement of the null-point position and a change of curvature of the inner and outer spine lines as indicated by the slight deviation of the computed outer spine from the observed one (Figure 3b). We further examine the influence of the bottom boundary used for extrapolation on the properties of the null-point. It is found that the height of the null-point systematically decreases by 1-2 Mm if the entire sunspot near the minor positive polarity is included.
The squashing degree Q, which measures the mapping of the field lines [80], is calculated by the method developed by Ref [81]. Taking advantage of the HMI vector magnetograms, the BPs are calculated by using the formula where B h and B z are the horizontal and vertical components of the vector magnetic field B, respectively. In addition, we also calculate BPs through the bottom boundary of extrapolated 3D potential field data. It is found that the BPs appearing in the observed vector field is absent in the extrapolated one, strongly indicating the existence of a twisted flux rope.

Data availability:
The datasets generated during and/or analysed during the current study are available from the corresponding author upon request.